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Abstract:

One aspect of the invention provides a spatially-selective disk including
a plurality of holes arranged such that a matrix having a plurality of
rows, each row having elements corresponding to a fraction of a pixel in
a viewing window projected onto the disk that is backed by a hole at a
distinct rotational position of the disk, has linearly independent rows.
Another aspect of the invention provides a spectrometry device including:
a disk having one or more holes; a motor configured to rotate the disk;
one or more beam-shaping optics arranged to map one or more spectral
components of radiation of interest onto a plurality of locations on the
disk; and a receiver positioned to capture the one or more spectral
components passing through the one or more holes as the disk is rotated.

Claims:

1. A spatially-selective disk comprising a plurality of holes arranged
such that a matrix having a plurality of rows, each row having elements
corresponding to a fraction of a pixel in a viewing window projected onto
the disk that is backed by a hole at a distinct rotational position of
the disk, has linearly independent rows.

2. A submillimeter imaging device comprising: a disk of claim 1; a motor
configured to rotate the disk; and a submillimeter wave receiver
positioned to capture waves passing through the one or more holes as the
disk is rotated.

4. The submillimeter imaging device of claim 2, further comprising:
submillimeter optics configured to focus the submillimeter waves on the
disk.

5. The submillimeter imaging device of claim 4, wherein the submillimeter
optics include one or more reflective surfaces.

6. The submillimeter imaging device of claim 4, wherein the submillimeter
optics include one or more refractive elements.

7. The submillimeter imaging device of claim 6, wherein the one or more
refractive elements are fabricated from polymethylpentene (PMP).

8. The submillimeter imaging device of claim 2, further comprising: a
shield defining a viewing window on the disk.

9. The submillimeter imaging device of claim 2, further comprising: one
or more additional receivers positioned to capture waves of a different
wavelength than the submillimeter wave receiver.

10. The submillimeter imaging device of claim 9, wherein the different
wavelength is a different range of submillimeter radiation than collected
by the submillimeter wave receiver.

11. The submillimeter imaging device of claim 9, wherein the different
wavelength is selected from the group consisting of: far-infrared, long
wave infrared, short wave infrared, visible light, and ultraviolet.

12. The submillimeter imaging device of claim 9, further comprising: an
integrating sphere positioned to diffuse waves passing through the one or
more holes as the disk is rotated for detection by the submillimeter wave
receiver and the one or more additional receivers.

13. A method of submillimeter imaging, the method comprising: providing:
a disk of claim 1; a motor configured to rotate the disk; and a
submillimeter wave receiver positioned to capture waves passing through
the one or more holes as the disk is rotated; actuating the motor to
rotate the disk; capturing a plurality of waves passing through the
plurality of holes as the disk rotates; solving a system of equations
wherein a magnitude of one of the plurality of reflections is equal to a
sum of a product of the reflection in each of a plurality of pixels and
the fraction of pixel area backed by the plurality of holes; and forming
an image from the plurality of the pixels.

14. A profiling scanner comprising: a proximal end; a distal end; a first
submillimeter imaging device of claim 2; and a second submillimeter
imaging device of claim 2.

15. A spectrometry device comprising: a disk having one or more holes; a
motor configured to rotate the disk; one or more beam-shaping optics
arranged to map one or more spectral components of radiation of interest
onto a plurality of locations on the disk; and a receiver positioned to
capture the one or more spectral components passing through the one or
more holes as the disk is rotated.

16. A method of spectrometry, the method comprising: providing the
spectrometry device of claim 15; actuating the motor to rotate the disk;
capturing a plurality of spectral components passing through the
plurality of holes as the disk rotates; and computing a spectrum by
solving a system of equations wherein a magnitude of one of the plurality
of spectral components is equal to a sum of a product of the spectral
component in each of a plurality of pixels and the fraction of pixel area
backed by the plurality of holes.

17. A spectrometry device comprising: a disk having a plurality of holes
and a contiguous aperture substantially opposite the plurality of hole; a
motor configured to rotate the disk; a mask defining an imaging window
and a spectrometry window; one or more beam-shaping optics arranged to
map one or more spectral components of radiation of interest received
through the imaging window and the holes and aperture of the disk onto a
plurality of locations on the disk; and a receiver positioned to capture
the one or more spectral components passing through the plurality of
holes and the aperture of the disk and the spectrometry window as the
disk is rotated.

18. A method of spectrometry, the method comprising: providing the
spectrometry device of claim 17; actuating the motor to rotate the disk;
capturing a plurality of spectral components passing through the
plurality of holes as the disk rotates; and computing a spectrum by
solving a system of equations wherein a magnitude of one of the plurality
of spectral components is equal to a sum of a product of the spectral
component in each of a plurality of pixels and the fraction of pixel area
backed by the plurality of holes.

19. A submillimeter imaging device comprising: a mask defining a
slit-shaped viewing window; a disk having a plurality of holes arranged
such that a matrix having a plurality of rows, each row having elements
corresponding to a fraction of a pixel in the viewing window projected
onto the disk that is backed by a hole at a distinct rotational position
of the disk, has linearly independent rows; a motor configured to rotate
the disk; a submillimeter wave receiver positioned to capture waves
passing through the one or more holes as the disk is rotated; and one or
more submillimeter optical elements actuatable to vary a portion of a
region of interest projected onto the viewing window such that a
two-dimensional image of a region of interest can be reconstructed by
capturing a plurality of one-dimensional images.

20. The submillimeter imaging device of claim 19, wherein the slit-shaped
view window is oriented radially with respect to a rotational axis of the
disk.

21. A method of submillimeter imaging, the method comprising: providing a
submillimeter imaging device of claim 19; actuating the motor to rotate
the disk; for each of a plurality of actuation positions of the
submillimeter optical elements: capturing a plurality of waves passing
through the plurality of holes as the disk rotates; solving a system of
equations wherein a magnitude of one of the plurality of reflections is
equal to a sum of a product of the reflection in each of a plurality of
pixels and the fraction of pixel area backed by the plurality of holes;
and forming a one-dimensional image from the plurality of the pixels; and
concatenating the one-dimensional images to form a two-dimensional image.

22. A profiling scanner comprising: a proximal end; a distal end; a first
submillimeter imaging device of claim 82 positioned at the proximal end;
and a second submillimeter imaging device of claim 82 positioned at the
distal end.

[0002] Focal plane arrays in the submillimeter wavelength are not yet
commercially available. Accordingly, there is a need for systems and
methods that facilitate for formation of images by utilizing existing
single submillimeter detectors.

[0003] The complexity of developing such scanning systems for
sub-millimeter waves is greater than it is for the scanning systems in
other regimes, such as visible and infrared radiation. First, the
wavelength is larger; therefore, the size and weight of these systems are
greater. Second, the radiation is not as abundant. Current scanning
systems for sub-millimeter waves are large in size and have image
formation rates of less than one frame per second.

[0004] Likewise, similar challenges are presented in the field of
spectrometry, in which there remains a continued need for spectrometry
devices at reduced costs (on a per unit and/or per computation basis)
that increase computational speed.

[0005] Accordingly, there is a need for submillimeter scanning systems and
spectrometry devices that can overcome these challenges.

SUMMARY OF THE INVENTION

[0006] One aspect of the invention provides a spatially-selective disk
including a plurality of holes arranged such that a matrix having a
plurality of rows, each row having elements corresponding to a fraction
of a pixel in a viewing window projected onto the disk that is backed by
a hole at a distinct rotational position of the disk, has linearly
independent rows.

[0007] This aspect of the invention can have a variety of embodiments. The
disk can be absorptive. The disk can be reflective. The disk can be
conductive.

[0008] The plurality of holes can have substantially equal diameters. The
radius of the plurality of holes can be greater than or equal to about
one wavelength of interest. The radius of the plurality of holes can be
between about one wavelength of interest and about two wavelengths of
interest.

[0009] The disk can have a substantially uniform thickness. The disk can
have a thickness of greater than or equal to about one wavelength of
interest. The disk can have a thickness of between about one wavelength
of interest and about three wavelengths of interest. The disk can have a
thickness of between about two wavelengths of interest and about three
wavelengths of interest. The disk can have a thickness of about 2.7112
wavelengths of interest.

[0010] The holes can have a profile selected from the group consisting of:
a circle, a triangle, and an n-gon.

[0011] Another aspect of the invention provides a submillimeter imaging
device including: a disk having a plurality of holes; a motor configured
to rotate the disk; and a submillimeter wave receiver positioned to
capture waves passing through the one or more holes as the disk is
rotated. The holes are arranged such that a matrix having a plurality of
rows, each row having elements corresponding to a fraction of a pixel in
a viewing window projected onto the disk that is backed by a hole at a
distinct rotational position of the disk, has linearly independent rows.

[0012] This aspect of the invention can have a variety of embodiments. The
submillimeter imaging device can further include a submillimeter wave
source. The submillimeter imaging device can further include
submillimeter optics configured to focus the submillimeter waves on the
disk.

[0013] The submillimeter wave optics can include one or more reflective
surfaces. The one or more reflective surfaces can include one or more
curved reflective surfaces. The one or more reflective surfaces can
include one or more flat reflective surfaces.

[0014] The submillimeter wave optics can include one or more refractive
elements. The one or more refractive elements can be substantially
transparent to submillimeter radiation. The one or more refractive
elements can be fabricated from polymethylpentene (PMP).

[0015] The motor can rotate the spatially-selective structure at about
1,800 revolutions per minute. The submillimeter wave receiver can
captures images at a rate of about 30 frames per second.

[0016] The submillimeter imaging device can further include a shield
defining a viewing window on the disk. The shield can include a
radiation-absorbing material. The shield can include a
radiation-reflecting material.

[0017] The submillimeter imaging device can further include a storage
device. The storage device can include memory. The storage device can
include one or more disks.

[0018] The submillimeter imaging device can include one or more additional
receivers positioned to capture waves of a different wavelength than the
submillimeter wave receiver. The different wavelength can be a different
range of submillimeter radiation than collected by the submillimeter wave
receiver. The different wavelength can be selected from the group
consisting of: far-infrared, long wave infrared, short wave infrared,
visible light, and ultraviolet. The submillimeter imaging device can
include a waveguide positioned to guide waves passing through the one or
more holes as the disk is rotated to the submillimeter wave receiver and
the one or more additional receivers. The submillimeter imaging device
can further include an integrating sphere positioned to diffuse waves
passing through the one or more holes as the disk is rotated for
detection by the submillimeter wave receiver and the one or more
additional receivers.

[0019] Another aspect of the invention can provide a method of
submillimeter imaging. The method includes: providing a disk having a
plurality of holes arranged such that a matrix having a plurality of
rows, each row having elements corresponding to a fraction of a pixel in
a viewing window projected onto the disk that is backed by a hole at a
distinct rotational position of the disk, has linearly independent rows,
a motor configured to rotate the disk, and a submillimeter wave receiver
positioned to capture waves passing through the one or more holes as the
disk is rotated; actuating the motor to rotate the disk; capturing a
plurality of waves passing through the plurality of holes as the disk
rotates; solving a system of equations wherein a magnitude of one of the
plurality of reflections is equal to a sum of a product of the reflection
in each of a plurality of pixels and the fraction of pixel area backed by
the plurality of holes; and forming an image from the plurality of the
pixels.

[0020] This aspect of the invention can have a variety of embodiments. The
method can further include storing the image. The method can further
include performing an image recognition method on the image.

[0021] The storing and forming steps can be performed on a computer. The
computer can be a general-purpose computer that has been
specially-programmed with software instructions for executing the storing
and forming steps.

[0022] Another aspect of the invention provides a profiling scanner
including: a proximal end; a distal end; a first submillimeter imaging
device; and a second submillimeter imaging device. The first
submillimeter imaging device includes: a first disk having a plurality of
holes arranged such that a matrix having a plurality of rows, each row
having elements corresponding to a fraction of a pixel in a viewing
window projected onto the disk that is backed by a hole at a distinct
rotational position of the disk, has linearly independent rows; a first
motor configured to rotate the first disk; and a first submillimeter wave
receiver positioned to capture waves passing through the one or more
holes as the first disk is rotated. The second submillimeter imaging
device includes: a second disk having a plurality of holes arranged such
that a matrix having a plurality of rows, each row having elements
corresponding to a fraction of a pixel in a viewing window projected onto
the disk that is backed by a hole at a distinct rotational position of
the disk, has linearly independent rows; a second motor configured to
rotate the second disk; and a second submillimeter wave receiver
positioned to capture waves passing through the one or more holes as the
second disk is rotated.

[0023] This aspect of the invention can have a variety of embodiments. The
profiling scanner can further include a moving walkway configured to
carry an individual from the proximal end to the distal end.

[0024] The profiling scanner can further include a storage device. The
storage device can include memory. The storage device can include one or
more disks.

[0025] The profiling scanner can further include a display device. The
display device can be selected from the group consisting of: a cathode
ray tube (CRT), a plasma display, a liquid crystal display (LCD), an
organic light-emitting diode display (OLED), a light-emitting diode (LED)
display, an electroluminescent display (ELD), a surface-conduction
electron-emitter display (SED), a field emission display (FED), a
nano-emissive display (NED), an electrophoretic display, a bichromal ball
display, an interferometric modulator display, and a bistable nematic
liquid crystal display.

[0026] Another aspect of the invention provides a spectrometry device
including: a disk having one or more holes; a motor configured to rotate
the disk; one or more beam-shaping optics arranged to map one or more
spectral components of radiation of interest onto a plurality of
locations on the disk; and a receiver positioned to capture the one or
more spectral components passing through the one or more holes as the
disk is rotated.

[0027] This aspect of the invention can have a variety of embodiments. The
one or more beam-shaping optics can be selected from the group consisting
of: prisms and cylinders. The spectrometry device can further include a
shield defining a viewing window on the disk. The shield can include a
radiation-absorbing material. The shield can include a
radiation-reflecting material.

[0028] The spectrometry device can include a storage device. The storage
device can include memory. The storage device can include one or more
disks.

[0029] The spectrometry device can include a processing device configured
to reconstruct the one or more spectral components captured by the
receiver to determine the spectral content of the radiation. The
processing device can be a computer. The computer can be a
general-purpose computer that has been specially-programmed with
software.

[0030] Another aspect of the invention provides a method of spectrometry.
The method includes: providing a disk having one or more holes, a motor
configured to rotate the disk, one or more beam-shaping optics arranged
to map one or more spectral components of radiation of interest onto a
plurality of locations on the disk, and a receiver positioned to capture
the plurality spectral components passing through the one or more holes
as the disk is rotated; actuating the motor to rotate the disk; capturing
a plurality of spectral components passing through the plurality of holes
as the disk rotates; and computing a spectrum by solving a system of
equations wherein a magnitude of one of the plurality of spectral
components is equal to a sum of a product of the spectral component in
each of a plurality of pixels and the fraction of pixel area backed by
the plurality of holes.

[0031] This aspect of the invention can have a variety of embodiments. The
method can further include displaying the spectrum. The spectrum can be
displayed on a display device selected from the group consisting of: a
cathode ray tube (CRT), a plasma display, a liquid crystal display (LCD),
an organic light-emitting diode display (OLED), a light-emitting diode
(LED) display, an electroluminescent display (ELD), a surface-conduction
electron-emitter display (SED), a field emission display (FED), a
nano-emissive display (NED), an electrophoretic display, a bichromal ball
display, an interferometric modulator display, and a bistable nematic
liquid crystal display.

[0032] The computing step can be performed on a computer. The computer can
be a general-purpose computer that has been specially-programmed with
software instructions for executing the storing and forming steps.

[0033] Another aspect of the invention provides a spectrometry device
including: a disk having a plurality of holes and a contiguous aperture
substantially opposite the plurality of hole; a motor configured to
rotate the disk; a mask defining an imaging window and a spectrometry
window; one or more beam-shaping optics arranged to map one or more
spectral components of radiation of interest received through the imaging
window and the holes and aperture of the disk onto a plurality of
locations on the disk; and a receiver positioned to capture the one or
more spectral components passing through the plurality of holes and the
aperture of the disk and the spectrometry window as the disk is rotated.

[0034] This aspect of the invention can have a variety of embodiments. The
one or more beam-shaping optics can be selected from the group consisting
of: prisms, cylinders, and mirrors. The mask can include a
radiation-absorbing material. The mask can include a radiation-reflecting
material.

[0035] The spectrometry device can further include a storage device. The
storage device can include memory. The storage device can includes one or
more disks.

[0036] The spectrometry device can include a processing device configured
to reconstruct the one or more spectral components captured by the
receiver to determine the spectral content of the radiation. The
processing device can be a computer. The computer can be a
general-purpose computer that has been specially-programmed with
software.

[0037] The aperture can be internal to the disk. The aperture can be
external to the disk.

[0038] Another aspect of the invention provides a method of spectrometry.
The method includes: providing: a disk having a plurality of holes and a
contiguous aperture substantially opposite the plurality of hole, a motor
configured to rotate the disk, a mask defining an imaging window and a
spectrometry window, one or more beam-shaping optics arranged to map one
or more spectral components of radiation of interest received through the
imaging window and the holes and aperture of the disk onto a plurality of
locations on the disk, and a receiver positioned to capture the one or
more spectral components passing through the plurality of holes and the
aperture of the disk and the spectrometry window as the disk is rotated;
actuating the motor to rotate the disk; capturing a plurality of spectral
components passing through the plurality of holes as the disk rotates;
and computing a spectrum by solving a system of equations wherein a
magnitude of one of the plurality of spectral components is equal to a
sum of a product of the spectral component in each of a plurality of
pixels and the fraction of pixel area backed by the plurality of holes.

[0039] This aspect of the invention can have a variety of embodiments. The
method can further include displaying the spectrum. The spectrum can be
displayed on a display device selected from the group consisting of: a
cathode ray tube (CRT), a plasma display, a liquid crystal display (LCD),
an organic light-emitting diode display (OLED), a light-emitting diode
(LED) display, an electroluminescent display (ELD), a surface-conduction
electron-emitter display (SED), a field emission display (FED), a
nano-emissive display (NED), an electrophoretic display, a bichromal ball
display, an interferometric modulator display, and a bistable nematic
liquid crystal display.

[0040] The computing step can be performed on a computer. The computer can
be a general-purpose computer that has been specially-programmed with
software instructions for executing the storing and forming steps.

[0041] The aperture can be internal to the disk. The aperture can be
external to the disk.

[0042] Another aspect of the invention provides a submillimeter imaging
device including: a mask defining a slit-shaped viewing window; a disk
having a plurality of holes arranged such that a matrix having a
plurality of rows, each row having elements corresponding to a fraction
of a pixel in the viewing window projected onto the disk that is backed
by a hole at a distinct rotational position of the disk, has linearly
independent rows; a motor configured to rotate the disk; a submillimeter
wave receiver positioned to capture waves passing through the one or more
holes as the disk is rotated; and one or more submillimeter optical
elements actuatable to vary a portion of a region of interest projected
onto the viewing window such that a two-dimensional image of a region of
interest can be reconstructed by capturing a plurality of one-dimensional
images.

[0043] This aspect of the invention can have a variety of embodiments. The
slit-shaped view window can be oriented radially with respect to a
rotational axis of the disk.

[0044] Another embodiment of the invention provides a method of
submillimeter imaging, the method comprising: providing a submillimeter
imaging device as described above; actuating the motor to rotate the
disk; for each of a plurality of actuation positions of the submillimeter
optical elements: capturing a plurality of waves passing through the
plurality of holes as the disk rotates, solving a system of equations
wherein a magnitude of one of the plurality of reflections is equal to a
sum of a product of the reflection in each of a plurality of pixels and
the fraction of pixel area backed by the plurality of holes, and forming
a one-dimensional image from the plurality of the pixels; and
concatenating the one-dimensional images to form a two-dimensional image.

[0045] Another embodiment of the invention provides a profiling scanner
including: a proximal end; a distal end; a first submillimeter imaging
device as described above positioned at the proximal end; and a second
submillimeter imaging device as described above positioned at the distal
end.

FIGURES

[0046] For a fuller understanding of the nature and desired objects of the
present invention, reference is made to the following detailed
description taken in conjunction with the accompanying drawing figures
wherein:

[0047] FIGS. 1A and 1B depict an embodiment of a one-dimensional
spatially-selective disk according to an embodiment of the invention;

[0048] FIG. 2 depicts a system incorporating a spatially-selective disk
according to an embodiment of the invention;

[0049]FIG. 3A depicts a conceptual sketch of a spatially-selective disk,
a mask, and a coherent detector according to an embodiment of the
invention;

[0050] FIG. 3B depicts another view of the disk and mask from the
perspective of radiation reflected by the optics according to an
embodiment of the invention;

[0051] FIG. 4 depicts a cross-section of the scattering geometry according
to an embodiment of the invention;

[0052] FIGS. 5A-5C depicts the three-dimensional geometry of the hole
structure in accordance with an embodiment of the invention (units are in
normalized λ);

[0053]FIG. 6 depicts the power transmission coefficient as a function of
hole radius for a hole depth of 2.7112λ;

[0054] FIGS. 7A-7C depict the cross-sections of the geometries used to
investigate the minimal proximity between holes (the depth of the holes
is 2.7112λ, the radius of the holes is 1λ, and the incident
field is the same as in the radius analysis);

[0055]FIG. 8 depicts the percent linearity error as a function of the
center to center separation of two identical holes;

[0056]FIG. 9 is a grouping of photographs depicting an imaging system
according to an embodiment of the invention;

[0057] FIG. 10 is a photograph of the target mounted on the translational
stage according to an embodiment of the invention;

[0058] FIG. 11A is an image reconstructed from the raster scan using an
imaging system according to an embodiment of the invention;

[0059] FIG. 11B is an image reconstructed from the linear measurement
using an imaging system according to an embodiment of the invention;

[0060] FIGS. 12A and 12B are schematics of a spatially-selective mask
device for imaging in two dimensions according to an embodiment of the
invention;

[0061]FIG. 13 depicts a profiling scanner incorporating the imaging
devices described herein according to an embodiment of the invention;

[0062] FIGS. 14 and 15 depict imaging methods according to embodiments of
the invention;

[0063] FIG. 16 depicts an exaggerated spatially-selective disk (wherein
the dark circles represent holes) and a nine-pixel viewing window
according to an embodiment of the invention;

[0064] FIG. 17 depicts a spectrometry device according to an embodiment of
the invention;

[0065] FIG. 18 depicts a spectrometry method according to an embodiment of
the invention;

[0066]FIG. 19 depicts an exaggerated spectrometry device and a six-pixel
viewing window according to an embodiment of the invention;

[0067] FIGS. 20A-20C depict the structure and operation of an imaging
spectrometer according to an embodiment of the invention;

[0068] FIGS. 21A and 21B depict disks for use in an imaging spectrometer
according to embodiments of the invention;

[0069] FIGS. 22A-22C provide a grouping of photographs depicting another
imaging system according to an embodiment of the invention;

[0070] FIGS. 23A-23C provide 32×32 pixel reconstructed images
created by the device of FIGS. 22A-22C of the targets depicted in inset
photographs;

[0071] FIGS. 24A-24C provide 64×64 pixel reconstructed images
created by the device of FIGS. 22A-22C of the targets depicted in inset
photographs in FIGS. 23A-23C;

[0072] FIG. 25 depicts an imaging system incorporating a
spatially-selective device according to another embodiment of the
invention;

[0073] FIG. 26A depicts a mask in the outline of a handgun; FIG. 26B is a
64×64 pixel reconstructed image of the handgun outline with
visualization contours; FIG. 26c is a 64×64 pixel reconstructed
image of the handgun outline without visualization contours;

[0074] FIG. 27A depicts a mask in the outline of the letter `M`; FIG. 26B
is a 64×64 pixel reconstructed image of the `M` outline with
visualization contours; FIG. 26c is a 64×64 pixel reconstructed
image of the `M` outline without visualization contours;

[0075]FIG. 28 depicts a multi-mode imaging device according to an
embodiment of the invention;

[0076]FIG. 29 depicts a multi-mode matched horn receiver coupled with a
plurality of receivers according to an embodiment of the invention;

[0077]FIG. 30 depicts an integrating sphere coupled with a plurality of
receivers according to an embodiment of the invention;

[0078] FIGS. 31A-31F depict various imaging window geometries according to
embodiments of the invention;

[0079] FIGS. 32A-E depict various pixel geometries according to
embodiments of the invention;

[0080] FIGS. 33A and 33B are a schematic and photograph, respectively, of
a spatially-selective device according to an embodiment of the invention;

[0082] The instant invention is most clearly understood with reference to
the following definitions:

[0083] As used in the specification and claims, the singular form "a,"
"an," and "the" include plural references unless the context clearly
dictates otherwise.

[0084] The term "far infrared" (also known as "FIR") is generally used to
describe the region of the electromagnetic spectrum between about 120
terahertz (1.2×1014 Hz) to about 400 terahertz
(4×1014 Hz), which corresponds to wavelength ranges between
about 2,500 nanometers and about 750 nanometers.

[0085] The term "long wavelength infrared" (also known as "LWIR" or
"IR-C") is generally used to describe the region of the electromagnetic
spectrum between about 20 terahertz (2×1013 Hz) to about 37.5
terahertz (3.75×1013 Hz), which corresponds to wavelength
ranges between about 15 micrometers and about 8 micrometers.

[0086] The term "short wavelength infrared" (also known as "SWIR" or
"IR-B") is generally used to describe the region of the electromagnetic
spectrum between about 100 terahertz (1×1014 Hz) to about 214
terahertz (2.14×1014 Hz), which corresponds to wavelength
ranges between about 3 micrometers and about 1.4 micrometers.

[0087] The term "submillimeter radiation" (also known as "terahertz
radiation", "terahertz waves", "terahertz light", "T-rays", "T-light",
"T-lux", and "THz") is generally used to describe the region of the
electromagnetic spectrum between about 300 gigahertz (3×1011
Hz) and about 3 terahertz (3×1012 Hz), which corresponds to
wavelength ranges between about 1 millimeter and about 100 micrometers.

[0088] The term "ultraviolet" is generally used to describe the region of
the electromagnetic spectrum between about 7.5×1014 Hz to
about 3×1016 Hz), which corresponds to wavelength ranges
between about 400 nanometers and about 10 nanometers.

[0089] The term "visible light" is generally used to describe the region
of the electromagnetic spectrum between about 400 terahertz
(4×1014 Hz) to about 790 terahertz (7.9×1014 Hz),
which corresponds to wavelength ranges between about 760 nanometers and
about 380 nanometers.

DESCRIPTION OF THE INVENTION

[0090] Spatially-selective disks are described along with systems and
methods utilizing spatially-selective disks. The spatially-selective
disks can be used to image targets using electromagnetic energy of a
various wavelengths referred to herein as the "wavelength(s) of
interest." Some embodiments of the invention provide an image forming
device that can be packaged into a handheld box and is capable of
scanning and forming images at video rates.

Spatially-Selective Disks

[0091] Referring now to FIG. 1, an embodiment of a one-dimensional
spatially-selective disk 100 is provided. The disk 100 includes a
plurality of holes 102 arranged on a substantially constant radius R from
the center C of the disk 100. The holes can be positioned randomly or
pseudorandomly along radius R. That is, the radial distance R between the
centers of holes 102 can be random or pseudorandom. The holes 102 can
also be positioned in a non-random pattern. The pattern however should
produce linearly independent measurements as described herein.

[0092] Holes 102 can be cylindrical, i.e., a ruled surface spanned by a
one-parameter family of parallel family of parallel lines. For example,
holes 102 can have a profile selected from the group consisting of: a
square, a rectangle, a triangle, a circle, an oval, a polygon, a
parallelogram, a rhombus, an annulus, a crescent, a semicircle, an
ellipse, a super ellipse, and a deltoid. Electromagnetic analysis can be
performed for particular hole profiles to determine suitable hole
dimensions for a particular shape. Preferably, the far field measurement
for given hole 102 should result from the field incident on the hole 102
and not from edge currents. Holes 102 in this embodiment in all other
disks described herein can be of uniform sizes and/or shapes or
nonuniform sizes and/or shapes.

[0093] Preferably, the linear edge-to-edge distance between adjacent holes
102 is greater or equal to a wavelength of interest. For example, the
edges of holes 102 can be separated by a linear distance ranging between
about 1 times to about 5 times a wavelength of interest λ (e.g.,
about 1.0, about 1.5, about 2.0, about 2.5, about 3.0, about 3.5, about
4.0, about 4.5, about 5.0 times a wavelength of interest λ).

[0094] In some embodiments, the plurality of holes 102 have substantially
equal diameters. In some embodiments, the radius of the holes 102 is
proportional the wavelength of interest. For example, holes 102 can have
radii ranging between about 0.2 to about 2.05 times a wavelength of
interest λ (e.g., about 0.25, about 0.50, about 0.75, about 1.00,
about 1.25, about 1.40, about 1.50, about 1.75, and about 2.00 times a
wavelength of interest λ).

[0095] Embodiments of the invention described herein can be utilized to
image radiation spanning a range of wavelengths. The electromagnetic
analyses described herein are equally applicable for such applications
and can be performed on the maximum wavelength in the range
(λmax). For example, holes capable of imaging a wavelength of
0.5 mm also can image wavelengths of 0.4 mm, 0.2 mm, and the like.

[0096] In some embodiments, disk 102 is fabricated from a material that is
reflective or absorptive of the wavelength of interest. In further
embodiments, disk 102 is fabricated from an electrically conductive
material. For example, the disk can be solid piece of metal such as
silver, gold, copper, aluminum, platinum, iron, and alloys thereof.

[0097] The disk 100 can have a substantially uniform thickness. In some
embodiments, the thickness is defined relative to the wavelength of
interest. For example, the disk 100 can have a thickness greater than or
equal to about one wavelength of interest (e.g., between about 1 and
about 3, between about 2 and about 3 times a wavelength of interest). In
one example, used for analysis of the invention, the disk 100 had a
thickness of 2.7112 times a wavelength of interest.

Imaging System

[0098] FIG. 2 depicts a system 200 incorporating a spatially-selective
disk 202. A submillimeter wave source 204 emits radiation at a desired
wavelength. Submillimeter wave source 204 exposes object of interest 206
with submillimeter waves, which are reflected to submillimeter optics
208. Submillimeter optics 208 direct the reflection to mask 210 that
defines an imaging window through which portion of the waves reach the
spatially-selective disk 202. As spatially-selective disk 202 is spun by
motor 212, holes (not depicted) are individually brought into the focal
plane of focusing mirror 208 and permit the submillimeter wave to reach
submillimeter receiver 214.

[0100] Gyrotrons are available from Communications & Power Industries of
Palo Alto, Calif.; Gyrotron Technology, Inc. of Bensalem, Pa.; Thales
Group of Neuilly-sur-Seine, France; and Toshiba Corporation of Tokyo,
Japan. Backward wave oscillators are described in U.S. Pat. No.
2,880,355. Far infrared lasers are available from Zaubertek, Inc. of
Oviedo, Fla., Laser 2000 GmbH of Munich, Germany, and Coherent, Inc. of
Santa Clara, Calif. Quantum cascade lasers are described in U.S. Pat.
Nos. 7,359,418 and 7,386,024 and U.S. Patent Application Publication Nos.
2008/0069164 and 2008/0219308. Free electron lasers are described in U.S.
Pat. No. 7,342,230. Synchrotron light sources are available from Lyncean
Technologies, Inc. of Palo Alto, Calif. Photomixing devices are described
in U.S. Pat. Nos. 7,105,820 and 7,326,930 and U.S. Patent Application
Publication Nos. 2005/0156110; 2006/0054824; and 2007/0229937. Integrated
submillimeter generators and detectors are available under the
PICOMETRIX® T-RAY® trademark from Advanced Photonix, Inc. of Ann
Arbor, Mich.

[0101] Submillimeter optics 208 can include one or more surfaces
configured to reflect submillimeter radiation (e.g., curved reflective
surfaces or flat reflective surfaces). Additionally or alternatively,
submillimeter optics 208 can include one or more refractive elements.
Refractive elements can be fabricated from a material that is
substantially transparent to submillimeter radiation such as
polymethylpentene (PMP) available under the TPX® trademark from
Mitsui Chemicals America, Inc. of Rye Brook, N.Y. Submillimeter optics
208 can include one or more focusing mirrors (also known as "concave
mirrors") are available from suppliers such as Edmund Optics Inc. of
Barrington, N.J. Focusing mirrors can composed of glass, metal, or other
materials capable of reflecting submillimeter radiation. Suitable mirrors
(e.g. gold-coated aluminum substrates) are available from RadiaBeam
Technologies, LLC of Marina Del Ray, Calif.

[0102] Motor 212 spins at a speed sufficient to produce a desired number
of frames per minute. For example, if the receiver 214 is to capture
images at a rate of 30 frames per second (the NTSC video standard), motor
212 can spin spatially-selective disk 202 at a rate of 1,800 revolutions
per minute. Other capture rates can be achieved and by altering the speed
of motor 212. Because one image is captured per revolution, the image
capture rate per second is equal to the rotational speed of the disk 202
(in revolutions per minute) divided by 60. Motor 210 can, in some
embodiments, be a servomechanical device capable of actuation to defined
rotational positions and/or capable of self-correction of deviations from
a desired rotational position and/or speed.

[0103] Motor 212 can, in some embodiments, be a DC motor that spins the
disk 202 at a controlled, constant speed. The motor 212 can also be a
brushless DC motor or a permanent magnet synchronous motor. The motor 212
can be any motor that can rotate the disk at a controlled constant speed
with or without the help of external sensors such as positional encoders,
hall sensors, and the like.

[0104] Mask 210 can, in some embodiments, be fabricated from a material
configured to absorb submillimeter radiation. Suitable absorptive
materials include ECCOSORB® materials (available from Emerson &
Cummings of Randolph, Mass.) and radar absorbent materials (RAM).
Alternatively, mask 210 can be fabricated from a material configured to
reflect submillimeter radiation.

[0108] Processor 220 is an electronic device (also known as a central
processing unit or microprocessor) capable of executing instructions
stored as hardware and/or software. Suitable processors are available
from manufacturers such as Intel Corporation of Santa Clara, Calif. or
Advanced Micro Devices (AMD) of Sunnyvale, Calif.

[0110] Referring now to FIG. 3A, a conceptual sketch of a
spatially-selective disk 302, a mask 310, and a coherent detector 314 is
depicted. As discussed herein, the disk 302 is formed by making a
sequence of holes 102 along a constant radius of a disk 302 (e.g., a disk
302 made from a conductive material such as metal). Mask 310 defines an
imaging window 316 that permits radiation to reach a portion of the disk
302. (Half of the mask 310 and imaging window 316 is omitted from FIG. 3A
in order to permit clearer visualization of disk 302.) Spinning the disk
302 (e.g., with a motor 312) scans the holes 102 through the image formed
on disk 302. A detector 314 placed behind the spinning disk 302 collects
radiation passing through the holes 102. The holes 102 can be arranged in
a pseudo-random pattern.

[0111] Referring now to FIG. 3B, another view of the disk 302 and mask 310
is provided from the perspective of radiation reflected by the optics.
The imaging window of the mask 310 is divided by arbitrary pixel dividers
318 into a plurality of pixels, each spanning an angle θp. The
center of each hole 102 can be defined in terms of polar coordinates
(rm, θm) relative to the center C of disk 102.

[0112] At each detector sample time, energy from a different pattern of
holes 102 is collected. These measurements constitute a linear
measurement of the energy in the image formed on the disk 302. This
process can be formalized mathematically and is expressed as

m= M p (1)

where m is a vector, the elements of which contain the values of the
measurements, M is a full rank matrix that encodes the pattern of the
holes on the disk for each measurement, and p is the unknown vector that
contains the pixel intensities. In compressive sensing terminology, M is
the measurement matrix and m is the measurement vector. The image is
reconstructed by solving this equation for p. Because M is a full rank
matrix, the solution is easy to compute. This device and the image
measurement and reconstruction technique are described in more detail in
Orges Furxhi & Eddie L. Jacobs, "A sub-millimeter wave line imaging
device," 7670 Proc. SPIE 76700L (Apr. 27, 2010).

[0113] A regularized linear least squares solution for p can be computed
to counter an ill-conditioned measurement matrix and/or a noisy
measurement. Additionally or alternatively, the truncated singular value
decomposition method can be utilized to solve Equation (1) for pixel
values p. Each of these methods is well known and described in standard
linear algebra textbooks.

[0114] The imager is configured similarly to a system with a focal plane
array and the image plane mask is positioned where the focal plane array
would be. Because the system is still a scanning system, the available
integration time per measurement per detector is much less than the
integration time available to the focal plane array detectors. This is
mitigated in part by the presence of many scanning holes per measurement
allowing more energy to go through and be measured by the detector. In
addition, if compressive imaging techniques are used, the image can be
reconstructed by taking less measurements than desired image pixels as
discussed in M. Duarte et al., "Single-pixel imaging via compressive
sampling," 25 IEEE Signal Processing Magazine 83-91 (March 2008) and J.
Romberg, "Imaging via compressive sampling," 25 IEEE Signal Processing
Magazine 14-20 (March 2008). This increases the integration time
available per measurement. The drawback of this technique is the slow
reconstruction time associated with the iterative compressive sensing
algorithms. This approach is not employed in this research; rather the
number of measurements is made equal to the number of desired pixels
allowing instantaneous reconstruction.

Design of Image Plane Mask

[0115] To design the image plane mask, three-dimensional electromagnetic
analysis was utilized. The three-dimensional structure of interest is
assumed to be a perfect electric conductor (PEC). The field incident on
the structure is an elliptically polarized tapered Gaussian beam given by
H. Braunisch et al., "Tapered wave with dominant polarization state for
all angles of incidence," 48 IEEE Trans. on Antennas and Propagation
1086-96 (July 2000). The observables of interest are the power incident
on the structure, the power reflected from the structure, and the power
transmitted by the structure.

[0116] The powers are obtained once the far incident and scattered fields
are known. The far incident field is derived using the stationary phase
approximation as discussed in L. Mandel, "Optical Coherence and Quantum
Optics" (1995). Using the incident field on the structure, the Electric
Field Integral Equation (EFIE) can be solved for the currents using the
Method of Moments (MoM) technique. The currents are used to find the far
scattered fields with the help of the far field approximation.

[0117] The main equations used in the analysis are summarized below. The
complete derivations of the equations and the numerical techniques used
are available in O. Furxhi, "Spatially Selective Mirrors and Masks for
Submillimeter Wave Imaging" (Doctoral Dissertation) (University of
Memphis) (2010).

[0118] To formalize the problem, the scattering object is assumed to be an
open scatterer. The open scatterer can be extended and deformed to adhere
to the scattering structure of interest. A cross-section of the
scattering geometry is depicted in FIG. 4. The scatterer is illuminated
with the Gaussian tapered beam from above (z>0). The incident field
induces currents on the scatterer which radiate. Therefore, the total
field anywhere in space is composed of the incident field and the
scattered field radiated by the scatterer

E(R)=Ei(R)+Es(R) (2)

[0119] The EFIE for the structure is obtained in the following manner. The
well-known vector wave equation is transformed into an integral equation
using the well-known vector form of Green's theorem and the free space
Green function dyad G0 given by

as described in C. Tai, "Dyadic Green's Functions in Electromagnetic
Theory" (1971), where I={circumflex over (x)}{circumflex over
(x)}+yy+{circumflex over (z)}{circumflex over (z)} is the unit dyad (or
idem factor), k2=ω2ε0μ0 is the free
space wave number, R=x{circumflex over (x)}+yy+z{circumflex over (z)} is
a vector in Cartesian space noting the observation point, R' is a vector
noting the source point, and

∇ = x _ ^ ∂ ∂ x +
y _ ^ ∂ ∂ y + z _ ^
∂ ∂ z ##EQU00002##

is the gradient operator. The Green function dyad satisfies the wave and
radiation equations as discussed by Tai. Using this fact and applying
vector identities as discussed in J. Jackson, "Classical Electrodynamics"
(1999), Equation (4) is obtained

where E(R) is the electric field in a volume V enclosed by the surface S,
{circumflex over (n)} is the outward normal to S, and H(R') is the
magnetic field on the surface contour.

[0120] Referring to FIG. 4, Equation (4) is applied to the following
fields in the respective regions: the scattered field in the volume
V.sup.+ enclosed by Ss.sup.+, Sc, and S.sub.∞.sup.+; and
the incident field in the volume V.sup.- enclosed by Ss.sup.-,
Sc, and S.sub.∞.sup.-. In all three cases, the integral over
S.sub.∞.sup.+/- vanishes because the scattered and incident fields
satisfy the radiation condition in the respective regions. Combining and
adding the three resulting equations as the contours Ss.sup.+ and
Ss.sup.- approach Ss and using Equation (2) results in

Equation (5) gives the scattered field in the volumes V.sup.+ and V.sup.in terms of the fields on the scatterer surface Ss. The superscripts
+ and - indicate fields above and below the scatterer in {circumflex over
(n)}' is the unit normal pointing into the unit normal pointing into
V.sup.+. This equation is made more specific by applying the well-known
PEC boundary conditions of the scatterer discussed in J. Volakis, "Finite
Element Method for Electromagnetics" (1998)

where Js is the surface current on the scatterer and the free space
Green function dyad is written explicitly. Equation (6) is used to find
the scattered field in the volume V once the surface currents are known.
The final form of the EFIE is obtained using Equation (2) in Equation (6)
and evaluation Equation (6) on the boundary of the PEC scatterer

The unknown currents are obtained by solving Equation (7) using the
Method of Moments.

[0121] The incident field on the scatterer is given by Equation (8) as
discussed in O. Furxhi, "Spatially Selective Mirrors and Masks for
Submillimeter Wave Imaging" (Doctoral Dissertation) (University of
Memphis) (2010).

This is a Gaussian beam with spatial center at the origin of the
coordinate system and e(θ,φ) and (θ,φ) are the
polarization vector and Gaussian spectrum respectively, as given in H.
Braunisch et al., "Tapered wave with dominant polarization state for all
angles of incidence," 48 IEEE Trans. on Antennas & Propagation 1086-96
(July 2000).

[0122] The far incident field is calculated from Equation (8) using the
method of stationary phase for double integrals as presented in Leonard
Mandel & Emil Wolf, "Optical Coherence and Quantum Optics" (1995). For
z>0 and,

[0123] The far field is obtained by approximating Equation (6) for the
large argument |R-R'| and making the far field approximation as discussed
in A. Ishimaru, "Electromagnetic Wave Propagation, Radiation, and
Scattering" (1991). The far scattered field is given by

[0124] Because of the conservation of energy, the power incident on the
structure is equal to the sum of powers reflected by and transmitted
through the structure. Because the structure is a perfect electric
conductor (PEC), there is no absorbed power. Therefore, as discussed in
O. Furxhi, "Spatially Selective Mirrors and Masks for Submillimeter Wave
Imaging" (Doctoral Dissertation) (University of Memphis) (2010):

[0125] For the numerical solution of Equation (7), the structure of
interest is modeled using triangular patches. The famous
Rao-Wilton-Glisson (RWG) basis functions described in S. Rao et al.,
"Electromagnetic scattering by surfaces of arbitrary shape," 30 IEEE
Trans. on Antennas & Propagation 409-18 (1982), are used as basis and
testing functions for the MoM. The resulting matrix equation is solved
using available software such as MATLAB® software (available from The
MathWorks, Inc. of Natick, Mass.). Once the surface currents on the
structure are found, the desired power quantities are calculated with the
help of the equations presented above.

[0126] Detailed explanations of the equations presented above and the
numerical methods associated with them are provided in O. Furxhi,
"Spatially Selective Mirrors and Masks for Submillimeter Wave Imaging"
(Doctoral Dissertation) (University of Memphis) (2010).

Electromagnetic Analysis Results and Design Parameters

[0127] The analysis method presented above can be used to design the
parameters of the scanning holes, namely the radius, depth, and minimal
proximity of the holes. As discussed in O. Furxhi, "Spatially Selective
Mirrors and Masks for Submillimeter Wave Imaging" (Doctoral Dissertation)
(University of Memphis) (2010), the depth of the holes does not have a
noticeable effect on the transmission of the radiation through the holes
as long as the radius of the hole is larger than the first cutoff radius
of a circular waveguide and the depth is comparable to the diameter of
the hole. For holes with radii less than the cutoff radius, transmission
decreases exponentially with depth.

[0128] Various embodiments of the invention demonstrated herein utilize
holes with large radii, i.e., radii greater than or equal to the largest
wavelength of interest. Therefore, from a design perspective, the hole
depth is a free parameter. In one embodiment, the thickness of the disks
was approximately 2.7112λ, where the wavelength λ=468.43
μm, corresponding to a frequency of 640 GHz. Because of this
restriction, the hole depth parameter is fixed.

[0129] As discussed, embodiments of the invention described herein can be
utilized to image radiation spanning a range of wavelengths. The
electromagnetic analyses described herein are equally applicable for such
applications and can be performed on the maximum wavelength in the range
(λmax).

[0130] The power transmission coefficient of the holes with depth
2.7112λ is investigated as a function of the hole radius. The
three-dimensional geometry of the structure used in this analysis is
depicted in FIGS. 5A-5C. The geometry is finite and has a diameter of
8λ. The incident field has a tapering of 1.5λ (the tapering
parameters is related to the variance of the Gaussian taper), is normally
incident, and is circularly polarized. The incident beam resembles a blur
spot approximately 5λ in diameter. Because the incident field is
tapered, the structure can be made finite and the transmission of the
hole can be measured. The radius of the hole is varied from 0.2λ to
2.05λ in steps of 0.05λ. The power transmission coefficient
is calculated as the ratio of the incident power on the top aperture of
the hole to the power transmitted in the lower hemisphere (z<0). The
results are shown in FIG. 6.

[0131] The transmission coefficients for certain radii are greater than
unity. The reason for this is that only the power incident on the hole
aperture from above is used as the input power reference. The fields
radiated by the edge currents at the hole apertures are not included in
the input power reference but they are accounted for in the far field
measurement. Hence, the calculated power transmission coefficient is
greater than unity. The edge current effects become less evident as the
radius increases. When the radius is larger than 1.4λ, these
effects are almost unnoticeable and therefore the far field measurement
results only from the power incident on the hole aperture. In this case,
the holes are said to scan the image formed on the image plane mask. This
is the desired effect because the radiation associated with the part of
the image formed on the hole should pass while the part of the image
outside the hole is blocked.

[0132] Another important parameter is the proximity between two holes.
This affects the linearity of the structure. Cross-sections of the
geometries used to investigate the minimal proximity are shown in FIGS.
7A-7C. The depth of the holes was 2.7112λ and the radius of the
holes was 1λ. For these hole parameters, the transmission
coefficient is unity. For a linear structure, the measurement from the
structure in FIG. 7A should be equal to the sum of the measurements from
the structures of FIGS. 7B and 7C. Because the source and the detector
are coherent, the power measurement is not expected to be linear.

[0133] To investigate the linearity of the structure as a function of the
separation distance, the percent linearity error metric is introduced.
The percent linearity error is calculated as the difference of the
measurement from the structure in FIG. 7A with the sum of the
measurements from the structures of FIGS. 7B and 7C. Then, the result is
divided by the sum of the measurements from the structures of FIGS. 7B
and 7C and multiplied by 100%. The results are depicted in FIG. 8.

[0134] Except when the holes are very close to each other (edge to edge
separation<λ) the linearity error oscillates around zero with a
period of 1λ. This error is predicted by the array factor of this
structure because the structure resembles two identical radiating
antennas separated by a distance as discussed in O. Furxhi, "Spatially
Selective Mirrors and Masks for Submillimeter Wave Imaging" (Doctoral
Dissertation) (University of Memphis) (2010) and C. Balanis, "Antenna
Theory" (1997). The error can be eliminated if many holes are placed at
random distances from each other. This is advantageous because it not
only improves the linearity of the structure but it also does not require
any modification of the scanning technique. The holes in the line imager
are placed in random fashion as required by the reconstruction technique.

[0135] From the results of the electromagnetic analysis, design parameters
for the holes in the image plane mask can be identified. The radii of the
holes are preferably greater than about 1.4λ, but other radii are
also possible such as about 1λ. In all these cases, the far field
measurement results from the field incident on the hole, and not from the
edge currents. In this case, the holes are effectively scanning the image
formed on the mask.

[0136] The edge to edge separation of the holes is preferably greater than
about 1λ. This separation assures that the only non-linearity is
due to the array factor of the structure.

[0137] The depth of the holes was determined based on the available disk
for the production of the mask. However, if the depth parameter is to be
designed, it should preferably be comparable with the diameter of the
holes and such that it does not introduce resonances (i.e., edge
currents). In general, so long as the radius and the depth of the holes
increase proportionally, transmission and linearity will be preserved.

WORKING EXAMPLE #1

Implementation of Imaging System

[0138] A grouping of photographs depicting an embodiment of the imaging
system described herein is provided in FIG. 9. A laboratory prototype of
the image plane mask device was implemented using parts from a 5.25 inch
hard drive. The hard drive platters were made of conducting materials and
were advantageously balanced and flat. The platters were used as the
disks 302 on which the scanning holes were drilled. The motor could be
driven at a constant rate and the disk was already mounted on the motor.
The motor was driven at three revolutions per second. The motor could
rotate at speeds up to 90 rotations per second using other electronics.

[0139] The front cover of the hard drive was removed and an imaging window
316 was placed in front of the scanning disk 302. The optical system
(comprised of folding mirrors 208a and elliptical mirror 208b) formed the
image on the imaging window 316, which was approximately 22 millimeters
long. An opening was made in the back of the case so that the radiation
was allowed to pass onto the receiver 314. An optical sensor 902 was
mounted in the vicinity of disk edge. This sensor 902 was used to trigger
a measurement for each rotation of the disk 302 and facilitated the
registration of the measurements with the position of the disk 302.

[0140] The receiver 314 and source 204 were obtained from Virginia Diodes,
Inc. of Charlottesville, Va. and operate at 640 GHz. The signal was
detected from the receiver 314 and down-converted to 4.8 GHz. The
down-converted signal was measured using the AGILENT® SCA AN1996A
spectrum analyzer available from Agilent Technologies, Inc. of Santa
Clara, Calif. The measurement data was transferred remotely to a computer
where it was stored and later post-processed to reconstruct the image.
For each rotation of the disk 302, 1000 data points were collected.

[0141] The optical system consisted of a main elliptical reflective
surface 208b with a focus at 1 meter and the other at 10 meters. The
image was formed on the 1 meter side. The system had an effective
diameter of 0.3048 meters (12 inch) and an effective focal length of
0.9091 meters, resulting in a F# of 2.9826. The magnification of the
system was 0.1, the depth of focus for coherent radiation was 0.01062
meters, and the depth of field for incoherent radiation was 1.0162
meters. The diffraction spot diameter was 3.75 millimeters for a
wavelength of 468.43 μm, corresponding to the illumination frequency
of 640 GHz. The system was folded using two flat mirrors 208a. The source
204 was placed three meters away from the object 206 to flood illuminate
it.

[0142] Holes were drilled on the disk 302 in a constant radius of 58
millimeters. This radius and the extent of the imaging window were chosen
to minimize the curvature of the scan. A single hole of radius 0.5
millimeters (1:06λ) is drilled at a distance from other holes that
have a radius of 1 millimeter (2.12λ) and are placed in the
vicinity of each other at a random order respecting the design parameters
presented above. The single hole was used to perform a raster scan of the
image formed on the imaging window. The radius of half a millimeter
allowed high transmission (over 98%) and high scan resolution. The disk
302 was 1.27 millimeters (2.7112λ) thick.

[0143] The imaging window 316 was placed over the disk 302 so that the
image is scanned vertically. For demonstration purposes, the object 206
was placed on a translational stage and was scanned horizontally.
Vertical lines of the image of the object were scanned by the image plane
mask as the object was moved horizontally and an image of it was
reconstructed when the measured data is post-processed.

WORKING EXAMPLE #2

Experimental Results of Imaging System

[0144] The letter "M" was imaged to investigate the capabilities of the
assembled imaging system. A photograph of the target mounted on the
translational stage is provided as FIG. 10. The object letter was formed
by placing a piece of carpet with a cutout of the letter "M" over a plate
of aluminum. The plate of aluminum was made rough to minimize specular
reflections. The contour of the letter "M" was approximately 15 to 20
millimeters wide. The height of the letter was 60 millimeters. Because of
the characteristics of the optical system, the image was expected to be
one tenth of the object in size and highly blurred. The target was made
small to ensure that it was illuminated uniformly by the source.
Illumination optics were not used; hence, the wavefront reaching the
object was not planar and images of large objects were not formed
properly.

[0145] The results of the raster scan (single hole) and linear measurement
scan (plurality of holes) are depicted in FIGS. 11A and 11B,
respectively. Referring to the raster scan image of FIG. 11A, which will
be used as the reference, the image is severely blurred. However, the
structure of the letter "M" can be identified. The blur was expected
given the characteristics of the optics. From the measurements, the image
has a height of 25 samples corresponding to 9.1 millimeters (the radius
where the holes are placed is 58 millimeters and 1000 data points were
collected per rotation). This is consistent with the calculation from the
parameters of the optical system, resulting in an object size of
approximately 60 millimeters.

[0146] FIG. 11B is the reconstructed image using the linear measurements
made on the image plane. There is a clear resemblance between the
reconstructed image and the raster scan image of FIG. 10A. The techniques
used to reconstruct the image are described in detail in. Orges Furxhi &
Eddie L. Jacobs, "A sub-millimeter wave line imaging device," 7670 Proc.
SPIE 76700L (Apr. 27, 2010) and O. Furxhi, "Spatially Selective Mirrors
and Masks for Submillimeter Wave Imaging" (Doctoral Dissertation)
(University of Memphis) (2010). To reconstruct the image, regularization
was used when inverting the measurement matrix because of the error in
the knowledge of the exact positions of the holes on the disk for each
data sample. The quality of the reconstruction will improve if all of the
energy that goes through the holes is measured.

Additional Embodiments

[0147] Current embodiments of the invention can perform line scans at
rates of three frames per second and post-process the data to reconstruct
the images.

[0148] Imaging can be improved by driving the hard drive spindle motor so
that the disk can be spun at least 30 revolutions per second. This will
facilitate video rate imaging.

[0149] The use of additional down-converters and an analog to digital
conversion card interfaced to a computer will facilitate the collection
of the measurement data and the real time image reconstruction.

[0150] Additionally, refined optics for the imager and illumination
systems will facilitate uniform plane wave illumination of the scene and
the minimization of aberrations. To collect all the energy that passes
through the holes, a lens can be placed behind the holes. The lens will
focus the energy on the horn of the receiving antenna.

[0151] One of the factors that affect the quality of the reconstructed
image is the uncertainty of the location of the holes. To mitigate this
uncertainty, precision machining can be used to drill the holes at known
locations.

[0152] The sensitivity of the imager can be improved if the image plane
mask is shielded properly from stray radiation that makes its way into
the receiver. This permits formation of images of objects that have low
reflectivity coefficients. Also, increasing the size of the imaging
window would allow for the formation of larger images. Because more
randomly placed holes will be contributing to the measurement, the
linearity of the measurement will improve. This will improve the quality
of the reconstruction.

[0153] The imager can be extended to full two-dimensional imaging by
replacing the slit imaging window with a rectangular imaging window and
by adding more randomly-placed holes on the disk. The image
reconstruction technique is the same as for the line image and has been
described in detail in Orges Furxhi & Eddie L. Jacobs, "A sub-millimeter
wave line imaging device," 7670 Proc. SPIE 76700L (Apr. 27, 2010) and O.
Furxhi, "Spatially Selective Mirrors and Masks for Submillimeter Wave
Imaging" (Doctoral Dissertation) (University of Memphis) (2010).
Preliminary analysis provided in O. Furxhi, "Spatially Selective Mirrors
and Masks for Submillimeter Wave Imaging" (Doctoral Dissertation)
(University of Memphis) (2010) demonstrates the ability to generate
enough random patterns in one revolution of the disk to reconstruct a 32
by 32 pixel image from linear measurements.

Two-Dimensional Imaging

[0154] FIGS. 12A and 12B provide a schematic of a spatially-selective mask
device 1200 for imaging in two dimensions. Device 1200 includes a disk
1202 having a plurality of holes 102 arranged in a random or
pseudo-random two-dimensional pattern. Disk 1202 is positioned behind a
mask 1210, which defines an imaging window 1216, and is spun by a motor
1212. Radiation selectively passes through holes 102 and is measured by
receiver 1214.

[0155] Referring to FIG. 12B, the imaging window 1216 is divided into a
plurality of pixels by pixel dividers 1218.

[0156] Equation (1) is valid for both the one-dimensional and
two-dimensional imaging problems. For the two dimensional image, the two
dimensional array of pixels are linearized and each row of the array is
concatenated to the end of the previous row. Just like for the line
imager, a full set of measurements can be collected during one full
rotation of the disk. Therefore, if the disk is rotated at a constant
rate of 1,800 rotations per minute the imager will produce images at a
video rate of 30 frames per second.

[0157] In some embodiments as depicted in FIG. 12B, the pixel block is a
square. In such an embodiment, the entries of the measurement matrix can
be calculated by the following method. The imaging window is divided into
conceptual square blocks as shown in FIG. 12B, each corresponding to an
image pixel. Each pattern of holes in the imaging window 1216 corresponds
to one row of the measurement matrix. Different patterns are obtained at
different rotational positions of the disk. For each pixel, a Monte Carlo
integration method is used to determine the area of intercept of that
pixel with the holes 102 inside the imaging window 1216. The ratio of the
area of intercept to the area of the pixel is the entry on the row of the
measurement matrix corresponding to that pattern and pixel.

[0158] Additionally or alternatively, analytical solutions can be
developed to determine the ratio of the area of intercept. The solution
depends on the relative position of the circle with respect to the square
and also on the radius of the circle with respect to the side of the
side. Such analytical have been implemented in MATLAB® software.

Scanning Applications

[0159] Embodiments of the invention can be utilized for standoff scanning
(e.g., at large gatherings such as sporting events, parades, rallies, and
the like.)

[0160] Other embodiments of the invention can be utilized for profiling
sensors that scan a single line of a moving object and form an image in
time. Such an embodiment can be deployed in environment such as airports,
office buildings, and the like where individuals are asked to move
through portal. Advantageously, profiling scanners only require the
imaging of a single line at any given moment. (The lines are then
combined to form an image.) Thus, the reflector size and computation
power for image acquisition can be minimized. Both multiple-modulation
and raster scanning embodiments described herein can be used in profiling
scanners.

[0161] Referring now to FIG. 13, a profiling scanner 1300 incorporating
the imaging devices described herein is provided. An individual 1302
enters the scanner 1300 at a proximal end 1304 and exits at a distal end
1306. The individual can move through the scanner 1300 by walking or can
stand on an optional moving walkway 1308. As the individual moves through
the scanner 1300, one or more imaging devices 1310a, 1310b images a
plurality of lines (e.g., substantially horizontal lines) of the
individual's body.

[0162] In some embodiments one or more optics 1312a, 1312b are used to
focus the imager. For example, the optics can 1312a, 1312b can focus on
the floor of the distal end 1306 and proximal end 1304, respectively. As
the individual 1302 moves through the scanner, the individual's entire
body will be imaged without the need to adjust the optics 1312.

[0163] In some embodiments, the profiling scanner 1300 or other scanning
device can be paired with or include a conventional optical camera. The
submillimeter wave line profile can be superimposed over the visible
image to provide more meaningful information (e.g., where contraband is
located on an individual).

Imaging Methods

[0164] FIG. 14 depicts an imaging method according to one embodiment of
the invention. In step S1402, an imaging device is provided, for example
an imaging device described herein. The imaging device can include
submillimeter wave optics, a spatially-selective structure, a motor
configured to rotate the spatially-selective structure, and a
submillimeter wave receiver as described herein. In step S1404, the motor
is actuated to rotate the spatially-selective disk. In step S1406, a
plurality of reflections is captured by the submillimeter wave receiver.
In step S1408, radiation is stored as a pixel. In step S1410, an image is
formed from a plurality of pixels.

[0165] In step S1412, the image can be processed with an image recognition
method capable of identifying suspicious items that could be a weapon or
contraband. Various suitable methods are known to those of skill in the
art and include edge detection algorithms and artificial intelligence
algorithms (e.g. neural nets) such as those described in U.S. Pat. Nos.
7,310,442 and 7,417,440 and U.S. Patent Application Publication No.
2008/0212742 and in Mohamed-Adel Slamani et al., "Image Processing Tools
for the Enhancement of Concealed Weapon Detection," 3 Proc. Int'l Conf.
on Image Processing 518-22 (October 1999). One or more privacy algorithms
can also be applied to the images to obscure sensitive regions such as
faces and/or human genitalia.

[0166] In step S1414, the image can be stored either by dedicated hardware
or software or by a general purpose computer programmed to acquire,
store, display, and/or transmit the images.

[0167] The images can be stored in variety of formats including known and
proprietary vector graphics formats such as vector graphics formats and
raster graphics formats. Vector graphics (also called geometric modeling
or object-oriented graphics) utilize geometrical primitives such as
points, lines, curves, and polygons to represent images. Examples of
vector graphics formats include the Scalable Vector Graphics (SVG) and
Vector Markup Language (VML) formats. The SVG format is defined at W3C,
Scalable Vector Graphics (SVG), http://www.w3.org/Graphics/SVG/. VML is
described in Brian Matthews, et al., Vector Markup Language (VML),
http://www.w3.org/TR/1998/NOTE-VML-19980513. Alternatively, the images
can be converted to or maintained in a raster graphics format, which is a
representation of images as a collection of pixels. Examples of raster
graphics formats include JPEG, TIFF, RAW, PNG, GIF, and BMP.

[0170] In step S1416, the images or video can be displayed on a display
device such as a cathode ray tube (CRT), a plasma display, a liquid
crystal display (LCD), an organic light-emitting diode display (OLED), a
light-emitting diode (LED) display, an electroluminescent display (ELD),
a surface-conduction electron-emitter display (SED), a field emission
display (FED), a nano-emissive display (NED), an electrophoretic display,
a bichromal ball display, an interferometric modulator display, a
bistable nematic liquid crystal display, and the like.

[0171] In step S1418, images can also be printed with devices such laser
printers, ink jet printers, dot matrix printers and the like.

[0172] As one will appreciate, the steps of the methods described herein
can be configured to place various steps in various orders and may
include additional steps or omit steps listed in FIG. 14. Specifically,
one of skill in the art will realize that image handling steps S1412,
S1414, S1416, and S1418 can be practiced various orders and/or
combinations.

[0173] FIG. 15 depicts another imaging method 1500. In step S902, an
imaging device is provided (e.g., an imaging device as described herein).
As the disk 1202 is rotated (S1504), receiver 1214 takes a number of
measurements equal to the number of arbitrary pixels in viewing window
1216 (S906). For example, in the nine-pixel embodiment, receiver 1214 can
take a measurement at 40° increments of rotation of disk 1202.

[0174] Measurements need not occur at regular intervals and need not
encompass a complete revolution of disk 1202. For example, in a
nine-pixel embodiment, receiver 1214 can take measurements at 10°
increments of rotation of disk 804 to obtain four 3×3 images. In
such an embodiment, measurements at 0°, 10°, 20°,
30°, 40°, 50°, 60°, 70°, and
80° are used to produce a first image; measurements at 90°,
100°, 110°, 120°, 130°, 140°,
150°, 160°, and 170° are used to produce a second
image; measurements at 180°, 190°, 200°,
210°, 220°, 230°, 240°, 250°, and
260° are used to produce a third image; and measurements at
270°, 280°, 290°, 300°, 310°,
320°, 330°, 340°, and 350° are used to
produce a fourth image.

[0175] The measurements used to generate consecutive images can overlap.
For example, if one seeks to obtain a plurality of 18×18 pixel
images, 324 measurements are required for each image. If measurements are
obtained at 1° increments, the first image can be obtained from
measurements from 0° to 323°, the second image can be
obtained from measurements from 324° of the first revolution to
286° of the second revolution, and so on.

[0176] Although it is possible to obtain series of images that are each
captured at a unique set of rotational positions, it may be preferable in
some embodiments to capture each image at the same set of rotational
positions (e.g., 1° increments from 0° to 323° on
each revolution) in order to minimize processing and storage requirements
by only storing a single, pre-calculated measurement matrix and its
inverse as discussed in U.S. Patent Application Publication No.
2010-0253783 and International Publication No. WO 2010/099328.

[0177] In order to produce a multi-pixel image, the fraction of the each
pixel area that is intersected by holes is calculated for each rotational
position at which a measurement is measured. For example, at the
rotational position depicted in FIG. 16, 40% of pixel p1, 15% of
pixel p2, 55% of pixel p3, 22% of pixel p4, 20% of pixel
p5, 8% of pixel p6, 43% of pixel p7, 36% of pixel p8,
and 70% of pixel p9 are backed by one or more holes 102. At this
first position, a measurement m1 is taken. This measurement m1
will reflect the signal reflected onto receiver 1214 by the portion of
viewing window 1216 that is backed by modulations as reflected in
equation (19) below.

This equation can be solved as part of a system of linear equations along
with the equations obtained at other rotational positions (S1508). These
equations can be expressed in matrix form as shown in equation (20) below
wherein dots (.) represent the coefficients in front of pixels
p1-p9 for the other positions of the disk 1202 and
m1-m9 represent the corresponding measured signal for each
position. As will be appreciated by one of skill in the art, the rows of
the matrix are preferably independent of each other, so that the system
of linear equations can be solved.

[0178] The 9×9 matrix in equation (20) is the measurement matrix
mentioned previously. For an image with n pixels, the measurement matrix
will have dimensions of n×n.

[0179] The values p1-p9 can be used to generate a multi-pixel
image (S1510). For example, values p1-p9 can be mapped to
grayscale values to produce a grayscale image. Alternatively, values
p1-p9 can be mapped to black or white to produce a
black-and-white image.

[0181] As will be appreciated by one of skill in the art, the systems and
methods described herein can be scaled to produce images larger than the
examples described herein. For example, to produce a 100×100 pixel
image, 10,000 measurements are obtained (corresponding to 10,000 distinct
modulation patterns). These measurements can be obtained by taking a
measurement every 0.036° (360°/10000).

Spectrometry Devices

[0182] Referring now to FIG. 17A, a spectrometry device 1700 is provided.
Spectrometry device 1700 includes a spatially-selective disk 1702 having
a plurality of holes 102 and spun by a motor 1712. Spectrometry device
1700 can also include a mask 1710 defining a viewing window 1716, a
receiver 1714, and/or one more beam-shaping optics 1720 arranged to map
one or more spectral components of radiation onto a plurality of
locations on the disk 1702. Optionally, optics 1713 such as a horn and/or
a lens can be positioned between disk 1702 and receiver 1714 to focus
radiation passing from disk 2002 on receiver 2014.

[0183] Spectrometry device 1700 can be constructed and operated in
accordance with the principles described herein. Receiver 1714 and
beam-shaping optics 1720 can be selected for a particular spectrum of
interest (e.g., optical light). For example, suitable beam-shaping optics
1720 for optical light can include prisms 1720a and cylinders 1720b.

[0184] Spectrometry device 1700 can be operated in accordance with
spectrometry method 1800 as depicted in FIG. 18 and further illustrated
in the context of FIG. 19.

[0185] In step S1702, a spectrometry device is provided (e.g., the
spectrometry devices 1700 described herein).

[0186] In step S1704, the disk is rotated (e.g., by actuating a motor
1712). As the disk is rotated, beam-shaping optics project one or more
spectral components of radiation onto a plurality of locations on the
disk within a viewing window. For example, as depicted in FIG. 19,
optical light can be projected onto pixels A-F corresponding to the
monochromatic colors red, orange, yellow, green, blue, and violet,
respectively.

[0187] In step S1706, a plurality of spectral components passing through
the plurality of holes are captured. As discussed below, the receiver
does not need to be able to discern between the spectral components
(e.g., distinguish whether the radiation is red light vs. orange light);
the receiver merely needs to be measure the relative intensity of the
radiation received at a given point in time.

[0188] In step S1708, a system of equations is solved as discussed above
in the context of FIG. 15 to compute a spectrum in step S1710. The
spectrum can then be processed (S1712), stored (S1714), displayed
(S1716), and/or printed (S1718) as discussed herein.

[0189] As will be readily appreciated by one of ordinary skill in the art,
the example depicted in FIG. 18 is highly simplified for ease of
illustration. Higher spectral resolution can be readily achieved by
sampling at higher rates in order to support an increased number of
pixels as discussed herein. The number of pixels in the image can be
increased since the pixels are non-physical; however a 64×64 pixel
image is sufficient for most stand-off applications of interest. Assuming
an F/1 optical system with one meter aperture and a Rayleigh wavelength
product 1.22λ=0.5 mm, the angular resolution of the imager is 0.5
milliradian. In an object space 100 meters away, this translates to a 5
cm resolution spot. Assuming one pixel sampling for resolution spot (two
per airy disk), a 64×64 pixel imager would image an object space
area of 3.2×3.2 meters square. This object space area is sufficient
to scan a highway lane, a few human targets, the trunk of a tree, or a
helicopter landing site.

Imaging Spectrometer

[0190] Referring now to FIGS. 20A-20C, an imaging spectrometer 2000 is
provided. When the imaging spectrometer 2000 operates in "imaging mode"
as discussed below, the imaging spectrometer 2000 forms an image of the
object of interest. When the imaging spectrometer 2000 operates in
"spectrometer mode" as discussed below, the imaging spectrometer 2000
constructs a spectrum of the object of interest.

[0191] The imaging spectrometer 2000 includes a disk 2002 having a
plurality of holes 102 positioned in a first region of the disk 2002 and
a larger aperture 2022 positioned on a second region of the disk 2002.
Imaging spectrometer also includes a motor 2012 configured to spin disk
2002, a mask 2010 defining an imaging window 2016 and a spectrometer
window 2024, and beam-shaping optics 2020 configured to guide radiation
from imaging window 2016 to spectrometer window 2024. Beam shaping optics
2020 can include, for example, prisms 2020a, cylinders 2020b, and mirrors
2020c, 2020d.

[0192] FIGS. 20A and 20B depict the operation of imaging spectrometer 2000
in spectrometry mode. Radiation from an object of interest (not depicted)
passes through the large aperture 2022 of disk 2002 and imaging window
2016, is directed by beam-shaping optics 2020, passes through one or more
holes 102 and spectrometer window 2024, and is measured by receiver 2014.
Optionally, optics 2013 such as a horn and/or a lens can be positioned
between disk 2002 and receiver 2014 to focus radiation passing from disk
2002 on receiver 2014.

[0193]FIG. 20c depicts the operation of the imaging spectrometer 2000 in
imaging mode. Radiation from an object of interest (not depicted) passes
through one or more holes of disk 2002 and imaging window 2016, is
directed by beam-shaping optics 2020, passes through large aperture 2022
of disk 2002 and spectrometer window 2024, and is measured by receiver
2014.

[0194] In both spectrometry and imaging modes, the images are
reconstructed according to the methods described herein (i.e., obtaining
a plurality of measurements at a plurality of rotational positions and
solving a system of equations.

[0195]FIG. 21A provides another depiction of the disk 2002 in imaging
spectrometer 2000. As depicted, aperture 2022 can be substantially
semi-circular and can be bounded by the outer perimeter of disk 2002.
Optionally, disk 2002 can include one or more weights 2026 positioned
adjacent to aperture 2022 to balance disk 2002 and promote uniform
rotation.

[0196] FIG. 21B depicts another embodiments of a disk 2002b. Instead of an
aperture 2022 defined within the perimeter of disk 2002b, disk 2002 is
generally semicircular, while still allows for attachment at is center
for rotation. Again, one or more weights 2026b can be used to
counterbalance the disk 2002. These weights 2026b can have a larger mass
than weights 2026 as they are mounted closer to the axis of rotation.

WORKING EXAMPLE #3

Further Implementations and Results of Imaging System

[0197] Referring now to FIGS. 22A-C, another embodiment of a
spatially-selective device 2200 was implemented using parts of a 5.25
inch hard drive. One of the platters of the hard drive was used as the
spinning disk 2202. The radius of the holes 102 and their minimal
separation were designed for operation at 640 GHz. A hole radius of 1 mm
and a minimal separation of 2 mm were chosen to guarantee unity
transmission, linearity, and the structural integrity of the disk, and to
utilize readily-available tools. With these parameters as restrictions, a
random pattern of 431 holes 102 was generated and the holes were drilled
in disk 2202 using a CNC mill.

[0198] The case 2220 of the hard drive was cut and modified for access to
the disk 2202 and for easy mounting on the optical stages. The
electronics of the motor driver were also modified so that the disk 2202
could be rotated at 3,000 rotations per minute. An emitter diode and
phototransistor pair 2222 were placed in the proximity of the disk 2202
to register the measurement samples with the corresponding hole patterns
in the imaging window 2216. The imaging window aperture was machined on
two slabs of aluminum 2210a, 2210b that were mounted to sandwich the disk
2202.

[0199] Although the device 2200 was designed for operation at terahertz
frequencies, it was paired with a visible light detector 2222 to form a
visible light imager. This establishes the proof of concept and the
frequency independence of the device. A picture of the setup for visible
light is shown in FIG. 22. A red laser source 2224 (400 nm-700 nm) was
collimated by collimating lens 2226 and was masked by object masks 2206
to form images over the imaging window 2216. An additional lens 2228 was
placed behind the disk 2202 and the imaging window 2216 to focus the
energy into an N-Type Silicon PIN Photodetector 2222. The optical path
from the collecting lens 2228 to the photodetector 2222 was enclosed by a
dark tube 2230 to eliminate stray light reaching the detector 2222. The
detector signal was sampled using a 16-bit data acquisition card from
Measurement Computing of Norton, Mass.

[0200] Three object masks 2206 were imaged and the reconstructed images
for two pixel resolutions are shown in FIGS. 23 and 24. For each
revolution of the disk 2202, 5,000 samples were recorded and filtered in
MATLAB® software using a low pass filter. For the 32×32 image,
1,024 staggered measurements were chosen and used to solve Equation (1)
for the unknown pixel values. For the 64×64 image, 4,096
consecutive measurements were used. Equation (1) was solved by
regularized matrix inversion which effectively acts as a low pass filter.

[0201] When displaying the images, the negative values are truncated (dark
spots in the images). The negative values in the reconstruction and the
low spatial frequency noise are attributed to signal noise, filtering
(and regularization), and error in the manufacturing of the disk that is
manifested in an incorrect measurement matrix. Minimizing noise and
manufacturing errors relaxes filtering and regularization and improves
reconstruction.

[0202] As the pixel resolution increases, image reconstruction improves.
This is expected because the finer sampling of the image decreases the
pixel-image ambiguity. It should be noted that the images are acquired,
reconstructed and displayed at video rates. The images can also be
reconstructed using compressive sensing methods and a portion of the
measurements. This is currently being investigated.

WORKING EXAMPLE #4

Further Implementations and Results of Imaging System

[0203] Referring now to FIG. 25, another embodiment of an imaging system
2500 incorporating a spatially-selective device 2200 as described in the
context of Working Example #3 was implemented using parts of a 5.25 inch
hard drive. One of the platters of the hard drive was used as the
spinning disk. The radius of the holes and their minimal separation were
designed for operation at 640 GHz. A hole radius of 1 mm and a minimal
separation of 2 mm were chosen to guarantee unity transmission,
linearity, and the structural integrity of the disk, and to utilize
readily-available tools. With these parameters as restrictions, a random
pattern of 431 holes was generated and the holes were drilled in the disk
using a CNC mill.

[0204] The case of the hard drive was cut and modified for access to the
disk and for easy mounting on the optical stages. The electronics of the
motor driver were also modified so that the disk could be rotated at
3,000 rotations per minute. An emitter diode and phototransistor pair
were placed in the proximity of the disk to register the measurement
samples with the corresponding hole patterns in the imaging window. The
imaging window aperture was machined on two slabs of aluminum that were
mounted to sandwich the disk.

[0205] The spatially-selective device was inserted in the imaging plane of
submillimeter wave receiver 2514 and the submillimeter wave receiver 2514
was placed behind the spatially-selective device 2200. The imager setup
is depicted in FIG. 25. A 640 GHz submillimeter wave source 2504 from
Virginia Diodes, Inc. of Charlottesville, Va. flood illuminates the
object of interest 2506. The object of interest 2506 reflects the
radiation toward a first folding mirror 2508a. The first folding mirror
2508a and the second folding mirror 2508b direct the radiation to an
elliptical mirror 2508c. The elliptical mirror 2508c focuses the
radiation onto the spatially-selective device 2200 to form an image of
the target on the spatially-selective device 2200. The
spatially-selective device 2200 scans the image and the radiation that
goes through the spatially-selective device 2200 is measured by the 640
GHz submillimeter wave receiver 2514. The receiver 2514 has an IF
(Intermediate Frequency) output at 4.8 GHz. The 4.8 GHz output is down
converted to another IF of 2.2 GHz and is fed into a spectrum analyzer
(model E4403B 9 KHz-3 GHz) from Agilent Technologies, Inc. of Santa
Clara, Calif. The spectrum analyzer applies a band pass filter and
amplifies the signal. The video output of the spectrum analyzer is then
sampled and digitized by a 16-bit data acquisition card from Measurement
Computing of Norton, Mass. (model: USB-2537). The spectrum analyzer and
the data acquisition card are triggered for each revolution of the disk.

[0206] The sampling rate of the data acquisition card was 250 KHz. The
disk was rotated at a constant speed of 3,000 rotations per minute (50
rotations per second). Accordingly, 5,000 measurements were recorded for
each rotation (or triggering event). The data acquisition card was
interfaced to a computer and the MATLAB® data acquisition toolbox was
used to retrieve the sampled data. The data was then low-pass filtered in
MATLAB® software and 4,096 consecutive samples were chosen and used
to solve Equation (1) for the unknown pixel values. Equation (1) was
solved using a regularized least squares solution of Equation

[0207] In Equation (22), α and βi are regularization
parameters. The matrices Hi are linear operations on the solution p.
The regularized least squares solution minimizes the norm of the solution
p and the norm of the matrix vector products Hip. Optimal values for
the regularization parameters exist and methods for finding them are
described in detail in inverse imaging and linear algebra literature such
as M. Bertero & P. Boccacci, "Introduction to Inverse Problems in Imaging
(1998). The linear operators Hi depend on the available prior
information on the solution p. For instance, if the solution (pixel
values) is expected to be smooth (which is the case for sub-millimeter
wave images), the operators Hi can be the Sobel or Prewitt (first
order derivatives) and the Laplacian (second order derivative) matrices
as described in image processing texts such as Rafael C. Gonzalez &
Richard E. Woods, "Digital Image Processing" (2007).

[0208] Images of two targets were formed on the spatially-selective mask,
measurements were taken and the images were reconstructed at video rates.
FIGS. 26A and 27A depict the targets, which consist of a plate of
aluminum covered by a gun mask and a mask of the letter `M`,
respectively. The masks were cut out of carpet, which scatters the
radiation so that very little of the radiation incident on the carpet
reaches the receiver 2514. The reconstructed images of the target
depicted in FIG. 26A are shown in FIGS. 26B and 26C and the reconstructed
images of the target depicted in FIG. 27A are shown in FIGS. 27B and 27C.
The regularized least squares solution was used. The minimized quantities
are the norm, the norm of the first derivative, and the norm of the
second derivative, the regularization parameters are 0.0001, 0.001, and
0.001, respectively.

[0209] There are several reasons for the low image quality. The
optical/elliptical mirror 2508c used is not optimal for this imaging
configuration. This contributes to the non-uniformity of the image, i.e.
the intensity of one part of the image is less than the intensity of
another part of the image. This can be observed in the image of the
letter `M` in FIGS. 27B and 27C, in which the legs of the letter `M` do
not appear in the image.

[0210] Another factor that contributes to the non-uniformity of the image
is the nature of active imaging; parts of the object perpendicular to the
optical axis reflect more than the parts that are not. The non-uniformity
due to the optical system can be remediated by weighting the measured
values prior to the image reconstruction. The weighting function will
depend on the characteristic of the optics. For example, the values from
the center of the image will be attenuated and the values from the edges
of the images will be amplified.

[0211] Another reason for the observed non-uniformity is the absence of an
energy collection mechanism. In the implementation shown in FIG. 25, the
receiver 2514 is placed quite far behind the mask 2200. This was done so
that the receiver 2514 could "see" the entire mask aperture. Preferably,
a matched horn, a lens, or an integrating sphere would couple the
receiver 2514 with the mask 2200. This increases the amount of signal
received and also allows the collection of all the energy, an assumption
inherent in the image reconstruction equations.

[0212] In addition to the reasons above, the regularization parameters in
the reconstruction were not optimal. The image reconstruction quality can
be improved by using optimal parameters.

Multi-Mode Imaging Devices

[0213] As discussed above in the context of Working Example #3 and Working
Example #4, the same spatially-selective deice is utilized to image
objects of interest with radiation of different wavelengths. This
demonstrates the frequency independence of the device. A multi-mode
imager can capitalize on this property. For example, several
submillimeter wave images (at different submillimeter wave frequencies),
far-infrared images, long wave infrared images, short wave infrared
images, visible light infrared images, and ultraviolet images can be
captured simultaneously or substantially-simultaneously by the imager. As
discussed herein, the spatially-selective disk should be configured to
accommodate the largest wavelength of interest.

[0214] Referring now to FIG. 28, another embodiment of the invention
provided a multi-mode imaging device 2800 for imaging an object of
interest 2806. Multi-mode imaging device 2800 includes many of the same
or similar elements (e.g., spatially-selective disk 2802, motor 2812,
horn 2813, receiver 2814, imaging window 2816, and reflective optics
2820) as other devices described herein.

[0216] Referring now to FIG. 29, an exemplary arrangement of horn 2813 and
multiple receivers 2814 is provided, which can be incorporated in the
multi-mode imaging device 2800 of FIG. 28. A reflective cone 2813 focuses
radiation on a matched waveguide 2902. A plurality of receivers 2814 are
positioned along the wave guide. Radiation of desired wavelengths is
permitted to exit the waveguide 2902 and enter individual receivers 2814
through the use of band-pass coatings 2904 at the interface between
waveguide 2814 and individual receivers 2814.

[0217] Referring now to FIG. 30, another horn 2813 can optionally be
replaced by an integrating sphere 3002 configured to diffuse radiation
received from imaging window 2816 via holes 102 in spatially-selective
disk 2802 for detection by multiple detectors 2814.

Exemplary Imaging Window and Pixel Shapes

[0218] Referring now to FIG. 31, the imaging window can have any shape. In
addition to the rectangular-shaped imaging windows depicted in FIGS. 12A,
17, 19-20C, 22A, and 28, the imaging window can, for example, have a
circular, semi-circular, wide rectangular (i.e., width>height), tall
rectangular (height>width), square (width=height) shape. Additionally,
the imaging window can be a horizontal or vertical slit (a slit being a
substantially rectangular opening having a dimension substantially equal
to a single pixel in one direction). In some embodiments, a vertical slit
can be positioned radially with respect to the rotational axis of the
disk such that the long axis of the vertical slit is colinear with a
radial line from the center of the disk to the perimeter of the disk.
Examples of various imaging window geometries are depicted in FIGS.
31A-F. FIG. 31A depicts a square imaging window. FIG. 31B depicts a
vertical slit imaging window. FIG. 31C depicts a horizontal slit imaging
window. FIG. 31D depicts a tall rectangular imaging window. FIG. 31E
depicts a wide rectangular imaging window. FIG. 31F depicts a circular
imaging window.

[0220] Referring now to FIGS. 33A and 33B, a spatially-selective device
similar to device 2200 described in Working Example #3 was further
evaluated.

[0221] In this configuration, the spatially-selective device was paired
with the sub-millimeter wave receiver to form images in transmission
mode. A schematic and photograph of this setup are shown in FIGS. 33A and
33B, respectively. A heterodyne source and receiver pair from Virginia
Diodes was used. The source and receiver operated at 640 GHz. In this
configuration, the 640 GHz source was placed one meter in front of the
device and was flood illuminating the imaging window. An object mask was
placed right before the imaging window and the projected image was
scanned by the spinning disk. The 640 GHz receiver was placed behind the
disk and measures the energy passing through the holes. The intermediate
frequency (IF) of the receiver was down converted from 4.8 GHz to 2.2 GHz
and this new IF was supplied to a spectrum analyzer. The spectrum
analyzer was used to band-pass filter and amplify the signal. A time
sweep of the signal triggered for each rotation was generated and the
video output of the spectrum analyzer was sampled at a rate of 250 KHz
using a 16-bit data acquisition card from Measurement Computing. The disk
rotated at 50 rotations per second and 5,000 samples were recorded per
rotation. The sampled signal was low-pass filtered using MATLAB®
software and 4,096 consecutive samples were used to reconstruct a
64×64 pixel image. One of the imaged masks and the corresponding
reconstructed image are shown in FIGS. 34A and 34B, respectively.

WORKING EXAMPLE #6

Use of Image Plane Coding for Submillimeter Imaging

[0222] Image plane coding is the process of encoding the information in
the image into a series of linear measurements over time, which is
processed to reconstruct the image. Each measurement is a linear
combination of many pixels in the image. Mathematically, the process is
described by

y=Mx+η (23)

where x is a vector representing the image, M is a matrix representing
the measurement process, η is a vector representing the noise in the
measurement process, and y is a vector of observed measurements. If N is
the number of pixels in the image x and M is the number of measurements
in y then M is a M×N matrix. For M<N, the solution to Equation
(23) involves iteration and hence is not suited for real time operation.
However, images of most objects of interest in the sub-millimeter wave
range will be limited in size due to the resolution restrictions of
diffraction. Accordingly, the case of M=N is suitable.

[0223] Engineering an imaging system from Equation (23) requires the
co-design of the measurement matrix M and an algorithm for reconstructing
the image {circumflex over (x)} from the measurements y. Because of
measurement noise, the reconstructed image will only be an approximation
of the real image x. Ill-conditioning in the measurement matrix amplifies
the noise in most reconstruction algorithms and hence also increases the
uncertainty in the estimate of image. These considerations are addressed
in inverse methods employing regularization. A generalized form of
Tikhonov regularization defined by Equation (23) has thus far proved most
successful with the methods of generating measurements and is described
further in Bertero & Boccacci.

x ^ = [ M T M + i μ i H i T H i
] - 1 M T y = Ry ( 24 ) ##EQU00021##

[0224] In Equation (24), the parameters μi--are Lagrangian
multipliers or the regularization parameters and the matrices Hi
define linear operations performed on the results. By appropriate choice
of these matrices and multipliers the effects of noise can be minimized
in the reconstruction. Two linear operators have proved successful thus
fare: the linear operator and the Laplacian operator. Note that once the
measurement matrix has been designed and the linear operators selected,
the matrix R is known so that image reconstruction is simply a matrix
multiplication.

Tilting-Optics Imaging Systems

[0225] The analysis presented above indicates that low condition number
measurement matrices are desired. For the coded aperture described
herein, the condition of the measurement matrix is strongly related to
the size of the disk and the number of measurements that are recorded for
each rotation of the disk. High pixel count images require an equally
high number of measurements. As the number of measurements increases, the
patterns used to form the linear equations become similar or correlated
and the equations become less independent. This results in an
ill-conditioned measurement matrix. Three approaches can be used to
mitigate this effect while keeping the resulting image pixel count
reasonable.

[0226] The first approach involves changing the size of the disk. The disk
size can be increased while holding the imaging window size constant and
positioned towards the perimeter of the disk. This will increase the arc
separation between measurements resulting in more variation in pattern
between measurements.

[0227] A second approach is turning the imager into a line imager and
coupling it with tilting optics (e.g., a tilting mirror) to form
two-dimensional images. For this purpose, the imaging window can be made
into a vertical slit. In this case, fewer measurements are acquired per
rotation and non-similar patterns are more abundant, thereby facilitating
linear independence between measurements and therefore good
reconstruction. The tilting mirror would have a small form factor and
would be placed immediately before the coded aperture. This approach also
increases the mechanical complexity of the system but keeps the form
factor of the system unchanged. In addition, a line imager is useful in
and of itself. For example, it can be used in conjunction with an optical
camera in a hallway to scan personnel for concealed objects using self
motion of the person to form the submillimeter image. The system could
then superimpose the submillimeter image on optical images as personnel
pass through the hallway.

[0228] A third approach is the use of Compressing Sampling (CS)
reconstruction methods as described in R. Baraniuk, "Compressive sensing
[lecture notes],"--24 IEEE Signal Processing Magazine, 118-21
(2007). In the CS approach, the number of measurement in one rotation of
the disk can be less than the number of pixels or k<n2. This
allows larger spacing between measurements and hence less correlation
between measurement matrix entries.

[0229] Although all three solutions are viable, the second solution is
particularly desirable due to the minimal modifications required to the
device and the simplification of the required computations. The condition
number of the line imager can be lowered even further if a different
pattern is implemented on the disk. A pattern that implements a Simplex
Code Mask (SCM) is possible with the line configuration. The measurement
matrix that results from an SCM consists of 1's and 0's. According to M.
Harwit and J. Sloane, "Hadamard Transform Optics" (1979), the SCM
measurement matrix is the matrix with the lowest condition number when
only entries of 0 and 1 can be used. The condition of the two-dimensional
imager can also be lowered using a different disk pattern.

Equivalents

[0230] The functions of several elements may, in alternative embodiments,
be carried out by fewer elements, or a single element. Similarly, in some
embodiments, any functional element may perform fewer, or different,
operations than those described with respect to the illustrated
embodiment. Also, functional elements (e.g., modules, databases,
computers, clients, servers and the like) shown as distinct for purposes
of illustration may be incorporated within other functional elements,
separated in different hardware, or distributed in a particular
implementation.

[0231] While certain embodiments according to the invention have been
described, the invention is not limited to just the described
embodiments. Various changes and/or modifications can be made to any of
the described embodiments without departing from the spirit or scope of
the invention. Also, various combinations of elements, steps, features,
and/or aspects of the described embodiments are possible and contemplated
even if such combinations are not expressly identified herein.

INCORPORATION BY REFERENCE

[0232] The entire contents of all patents, published patent applications,
and other references cited herein are hereby expressly incorporated
herein in their entireties by reference.

Patent applications by Eddie L. Jacobs, Memphis, TN US

Patent applications by Orges Furxhi, Memphis, TN US

Patent applications by THE UNIVERSITY OF MEMPHIS RESEARCH FOUNDATION

Patent applications in class OF LIGHT REFLECTION (E.G., GLASS)

Patent applications in all subclasses OF LIGHT REFLECTION (E.G., GLASS)